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X₂₁₃₁¶

ISOGONAL CONJUGATE OF X₂₁₃₀

X₂₁₃₁ is the isogonal conjugate of X₂₁₃₀.

X₂₁₃₁ (ISOGONAL CONJUGATE OF X₂₁₃₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2131 = ISOGONAL CONJUGATE OF X_2130."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02131(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2131 = ISOGONAL CONJUGATE OF X_2130 on reference triangle ABC."""
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center"])
            X_2130 = point_from_barycentrics(model, A, B, C, 0.19373197, 0.27423005, 0.53203798, ID="X_2130", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_3355 = point_from_barycentrics(model, A, B, C, 0.50188901, 0.4191657, 0.078945292, ID="X_3355", classes=["center"])
            central_line(model, X_20, X_2130, 20, 2130)
            central_line(model, X_3, X_3355, 3, 3355)
            X_2131 = intersect_lines(model, X_20, X_2130, X_3, X_3355, ID="X_2131", classes=["selected", "target"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_3472 = point_from_barycentrics(model, A, B, C, 0.34317873, 0.36369686, 0.2931244, ID="X_3472", classes=["center", "incident"])
            central_line(model, X_40, X_3472, 40, 3472, incident=True)
            return promote_point_to_top(model, X_2131)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2131 on the given reference triangle."""
            model = create_model('X_2131 = ISOGONAL CONJUGATE OF X_2130')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02131(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02131.json"))
            write_center_svg(
                model_acute,
                here / "x-02131.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2131¶

X₂₁₃₁¶